Data for Study 1 was collected in Fall 2015. Data for Study 2 was collected in Fall 2016 (hypotheses were preregistered at aspredicted.org).

In Study 1:
- 101 subjects participated
- 8 subjects’ AP data was discarded (see “Study1_badsubsAP.txt”)
- 9 subjects’ WIT data was discarded (see “Study1_badsubsWIT.txt”)
This left 93 subjects with AP data and 92 subjects with WIT data.

Additionally, IMS/EMS data is missing for subs 3, 27, 53, 82, 88, 89, 90, and 101.

In Study 2:
- 206 subjects participated
- 8 subjects’ AP data was discarded (see “Study2_badsubsAP.txt”)
- 7 subjects’ WIT data was discarded (see “Study2_badsubsWIT.txt”)
This left 198 subjects with AP data and 199 subjects with WIT data.

Additionally, IMS/EMS data is missing for 111, 189, and 201.

There were 48 trials for each condition in each task. In Study 2, each task was split into two sections so that participants could answer anxiety questions in the middle and end of each task.

1. Accuracy in each task:

2 (Prime: Black/White) x 2 (Target: gun/tool or positive/negative) rANOVA

Only showing interaction indicating racial bias (Prime x Target). For calculation of effect sizes, see “7 Effect sizes.R”
#### Study 1:
WIT

##                      Df Sum Sq Mean Sq F value   Pr(>F)    
## PrimeType:TargetType  1   2883  2882.9    96.5 5.97e-16 ***
## Residuals            91   2719    29.9                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AP

##                               Df Sum Sq Mean Sq F value Pr(>F)    
## PrimeType:TargetType           1   1794  1794.3  39.797  1e-08 ***
## PrimeType:TargetType:Observer  1     43    42.5   0.943  0.334    
## Residuals                     91   4103    45.1                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Study 2:

Only showing interaction indicating racial bias (Prime x Target). For calculation of effect sizes, see “7 Effect sizes.R”
WIT

##                       Df Sum Sq Mean Sq F value Pr(>F)    
## PrimeType:TargetType   1   3861    3861   120.7 <2e-16 ***
## Residuals            198   6331      32                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AP

##                       Df Sum Sq Mean Sq F value   Pr(>F)    
## PrimeType:TargetType   1   2478  2478.3   54.86 3.71e-12 ***
## Residuals            197   8900    45.2                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2. Comparing accuracy across tasks

- Correlation between performance bias scores
- Look at 3 way Prime x Target x Task interaction

Study 1

Excludes subjects that don’t have data in both tasks (only includes sample of 90).

A. Correlation between performance bias scores on each task

## 
## Call:
## lm(formula = APStand ~ WITStand, data = s1.perfBias)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.25273 -0.64697 -0.04138  0.68037  2.40625 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -9.621e-17  1.042e-01   0.000   1.0000  
## WITStand     1.851e-01  1.048e-01   1.767   0.0807 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9883 on 88 degrees of freedom
## Multiple R-squared:  0.03427,    Adjusted R-squared:  0.02329 
## F-statistic: 3.123 on 1 and 88 DF,  p-value: 0.08068

B. Examine 3 way Prime x Target x Task interaction

## Saving 7 x 5 in image
##                        Df Sum Sq Mean Sq F value   Pr(>F)    
## PrimeType:ConType:Task  1    992   991.7   23.04 6.35e-06 ***
## Residuals              89   3830    43.0                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Study 2

Excludes subjects that don’t have data in both tasks (only includes sample of 195).

A. Correlation between performance bias scores on each task

## 
## Call:
## lm(formula = APStand ~ WITStand, data = s2.perfBias)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.1856 -0.6008 -0.0491  0.5380  4.4047 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 3.394e-16  6.594e-02   0.000        1    
## WITStand    4.065e-01  6.611e-02   6.149 4.46e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.916 on 191 degrees of freedom
## Multiple R-squared:  0.1653, Adjusted R-squared:  0.1609 
## F-statistic: 37.82 on 1 and 191 DF,  p-value: 4.456e-09

B. Examine 3 way Prime x Target x Task interaction

## Saving 7 x 5 in image
##                         Df Sum Sq Mean Sq F value Pr(>F)    
## PrimeType:ConType:Task   1   3123  3123.3   94.02 <2e-16 ***
## Residuals              192   6378    33.2                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

3. Look at correlations between PDP estimates

Study 1:

## 
## Call:
## lm(formula = WIT_MeanC.stand ~ AP_MeanC.stand, data = s1.widePDP)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.77991 -0.52543  0.04554  0.59056  1.68756 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    4.088e-16  8.353e-02   0.000        1    
## AP_MeanC.stand 6.157e-01  8.400e-02   7.329 1.06e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7925 on 88 degrees of freedom
## Multiple R-squared:  0.379,  Adjusted R-squared:  0.372 
## F-statistic: 53.72 on 1 and 88 DF,  p-value: 1.062e-10

## 
## Call:
## lm(formula = WIT_AResid.stand ~ AP_AResid.stand, data = s1.widePDP)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.64807 -0.47586  0.03648  0.71495  2.42030 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)  
## (Intercept)     -9.771e-17  1.030e-01   0.000   1.0000  
## AP_AResid.stand  2.349e-01  1.036e-01   2.267   0.0258 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9775 on 88 degrees of freedom
## Multiple R-squared:  0.05519,    Adjusted R-squared:  0.04445 
## F-statistic:  5.14 on 1 and 88 DF,  p-value: 0.02583

## Saving 7 x 5 in image
## 
## Call:
## lm(formula = WITestimate ~ APTestimate * Type, data = compareAC)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.64807 -0.49558  0.03792  0.65228  2.42030 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)   
## (Intercept)           -1.629e-16  9.380e-02   0.000  1.00000   
## APTestimate            2.349e-01  9.432e-02   2.491  0.01368 * 
## TypePDP-C              5.879e-16  1.326e-01   0.000  1.00000   
## APTestimate:TypePDP-C  3.807e-01  1.334e-01   2.854  0.00483 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8898 on 176 degrees of freedom
## Multiple R-squared:  0.2171, Adjusted R-squared:  0.2038 
## F-statistic: 16.27 on 3 and 176 DF,  p-value: 2.233e-09

Study 2:

## 
## Call:
## lm(formula = WIT_MeanC.stand ~ AP_MeanC.stand, data = s2.widePDP)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.79597 -0.54572  0.03667  0.51197  1.86599 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -1.645e-16  5.468e-02    0.00        1    
## AP_MeanC.stand  6.527e-01  5.482e-02   11.91   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7596 on 191 degrees of freedom
## Multiple R-squared:  0.426,  Adjusted R-squared:  0.423 
## F-statistic: 141.7 on 1 and 191 DF,  p-value: < 2.2e-16

## 
## Call:
## lm(formula = WIT_AResid.stand ~ AP_AResid.stand, data = s2.widePDP)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3346 -0.6315 -0.0074  0.6270  2.3417 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     1.869e-17  6.973e-02   0.000 1.000000    
## AP_AResid.stand 2.577e-01  6.991e-02   3.685 0.000298 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9688 on 191 degrees of freedom
## Multiple R-squared:  0.06639,    Adjusted R-squared:  0.0615 
## F-statistic: 13.58 on 1 and 191 DF,  p-value: 0.0002975

## Saving 7 x 5 in image
## 
## Call:
## lm(formula = WITestimate ~ APTestimate * Type, data = compareAC)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.33459 -0.57549  0.01939  0.57615  2.34165 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            8.660e-17  6.266e-02   0.000        1    
## APTestimate            2.577e-01  6.282e-02   4.101 5.02e-05 ***
## TypePDP-C             -2.384e-16  8.861e-02   0.000        1    
## APTestimate:TypePDP-C  3.950e-01  8.884e-02   4.446 1.15e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8705 on 382 degrees of freedom
## Multiple R-squared:  0.2462, Adjusted R-squared:  0.2403 
## F-statistic: 41.59 on 3 and 382 DF,  p-value: < 2.2e-16

4. Test Observer x IMS interaction on three criterion (response accuracy bias, PDP-C, and PDP-A)

IMS is standardized for models, although not in plots. Models give unstandardized estimates.
#####Study 1:

Perf bias:

Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0849414 0.0199339 4.2611459 0.0000348
scale(IMS) -0.0165254 0.0178931 -0.9235635 0.3571219
ObserverPresent 0.0327737 0.0283822 1.1547277 0.2499454
TaskWIT 0.0403840 0.0281908 1.4325217 0.1539701
scale(IMS):ObserverPresent 0.0140434 0.0295156 0.4757948 0.6348777
scale(IMS):TaskWIT 0.0264328 0.0253047 1.0445810 0.2978122
ObserverPresent:TaskWIT -0.0526667 0.0401385 -1.3121244 0.1913812
scale(IMS):ObserverPresent:TaskWIT -0.0166459 0.0417413 -0.3987865 0.6905890

PDP-C estimates:

Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.3643438 0.0316063 11.5275674 0.0000000
scale(IMS) 0.0256741 0.0283705 0.9049588 0.3668650
ObserverPresent 0.0206224 0.0450014 0.4582618 0.6473940
TaskWIT 0.0104926 0.0446981 0.2347437 0.8147116
scale(IMS):ObserverPresent -0.0285231 0.0467985 -0.6094881 0.5430764
scale(IMS):TaskWIT -0.0269280 0.0401219 -0.6711537 0.5031026
ObserverPresent:TaskWIT -0.0364566 0.0636417 -0.5728422 0.5675659
scale(IMS):ObserverPresent:TaskWIT 0.0298970 0.0661831 0.4517325 0.6520812

PDP-A estimates:

Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0028778 0.0232003 0.1240425 0.9014393
scale(IMS) 0.0008643 0.0208251 0.0415018 0.9669483
ObserverPresent 0.0143705 0.0330329 0.4350368 0.6641294
TaskWIT 0.0236290 0.0328102 0.7201722 0.4724830
scale(IMS):ObserverPresent 0.0443437 0.0343520 1.2908630 0.1986368
scale(IMS):TaskWIT 0.0272456 0.0294511 0.9251118 0.3563185
ObserverPresent:TaskWIT -0.0721764 0.0467155 -1.5450194 0.1243422
scale(IMS):ObserverPresent:TaskWIT -0.1143868 0.0485810 -2.3545568 0.0197741
# Look at each level of observer separately
## Present
lm(AResid ~ scale(IMS)*Task, data = s1.wide[s1.wide$Observer == "Present",]) %>%
  summary()
## 
## Call:
## lm(formula = AResid ~ scale(IMS) * Task, data = s1.wide[s1.wide$Observer == 
##     "Present", ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.39115 -0.09930  0.01505  0.10830  0.31012 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)  
## (Intercept)         0.01413    0.02355   0.600   0.5502  
## scale(IMS)          0.03902    0.02370   1.647   0.1036  
## TaskWIT            -0.04254    0.03331  -1.277   0.2053  
## scale(IMS):TaskWIT -0.07522    0.03351  -2.244   0.0276 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1508 on 78 degrees of freedom
##   (8 observations deleted due to missingness)
## Multiple R-squared:  0.07884,    Adjusted R-squared:  0.04341 
## F-statistic: 2.225 on 3 and 78 DF,  p-value: 0.09182
## Absent
lm(AResid ~ scale(IMS)*Task, data = s1.wide[s1.wide$Observer == "Absent",]) %>%
  summary()
## 
## Call:
## lm(formula = AResid ~ scale(IMS) * Task, data = s1.wide[s1.wide$Observer == 
##     "Absent", ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.39653 -0.08642 -0.00636  0.09551  0.35744 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)
## (Intercept)        0.0029360  0.0230467   0.127    0.899
## scale(IMS)         0.0009669  0.0231851   0.042    0.967
## TaskWIT            0.0254624  0.0325930   0.781    0.437
## scale(IMS):TaskWIT 0.0304796  0.0327887   0.930    0.355
## 
## Residual standard error: 0.1494 on 80 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.02973,    Adjusted R-squared:  -0.00665 
## F-statistic: 0.8172 on 3 and 80 DF,  p-value: 0.4881
# simple slopes
lm(scale(AResid) ~ scale(IMS), data = s1.wide[s1.wide$Observer == "Present" & s1.wide$Task == "APT",]) %>%
  summary()
## 
## Call:
## lm(formula = scale(AResid) ~ scale(IMS), data = s1.wide[s1.wide$Observer == 
##     "Present" & s1.wide$Task == "APT", ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.03036 -0.69571  0.04235  0.46939  2.09364 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  0.03924    0.15036   0.261   0.7955  
## scale(IMS)   0.26510    0.15223   1.741   0.0895 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9628 on 39 degrees of freedom
##   (4 observations deleted due to missingness)
## Multiple R-squared:  0.07215,    Adjusted R-squared:  0.04836 
## F-statistic: 3.032 on 1 and 39 DF,  p-value: 0.0895
lm(scale(AResid) ~ scale(IMS), data = s1.wide[s1.wide$Observer == "Present" & s1.wide$Task == "WIT",]) %>%
  summary()
## 
## Call:
## lm(formula = scale(AResid) ~ scale(IMS), data = s1.wide[s1.wide$Observer == 
##     "Present" & s1.wide$Task == "WIT", ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.2584 -0.4911  0.1650  0.6393  1.6146 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.04591    0.14301  -0.321    0.750
## scale(IMS)  -0.21030    0.14478  -1.452    0.154
## 
## Residual standard error: 0.9157 on 39 degrees of freedom
##   (4 observations deleted due to missingness)
## Multiple R-squared:  0.05132,    Adjusted R-squared:  0.02699 
## F-statistic:  2.11 on 1 and 39 DF,  p-value: 0.1544
Study 2:

Perf bias:

Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0606414 0.0131239 4.6206923 0.0000053
scale(IMS) -0.0090080 0.0124408 -0.7240669 0.4694798
ObserverPresent 0.0332584 0.0190066 1.7498343 0.0809714
TaskWIT 0.0355513 0.0185600 1.9154856 0.0561970
scale(IMS):ObserverPresent -0.0159428 0.0192768 -0.8270496 0.4087391
scale(IMS):TaskWIT -0.0101322 0.0175940 -0.5758906 0.5650373
ObserverPresent:TaskWIT -0.0413698 0.0268794 -1.5390890 0.1246327
scale(IMS):ObserverPresent:TaskWIT 0.0277632 0.0272615 1.0184042 0.3091478

PDP-C estimates:

Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.3355554 0.0233887 14.3468823 0.0000000
scale(IMS) 0.0402489 0.0221714 1.8153523 0.0702749
ObserverPresent -0.0003638 0.0338727 -0.0107404 0.9914363
TaskWIT 0.0595237 0.0330767 1.7995666 0.0727393
scale(IMS):ObserverPresent -0.0049051 0.0343541 -0.1427815 0.8865400
scale(IMS):TaskWIT -0.0110335 0.0313551 -0.3518874 0.7251219
ObserverPresent:TaskWIT 0.0228862 0.0479032 0.4777597 0.6331019
scale(IMS):ObserverPresent:TaskWIT -0.0113101 0.0485841 -0.2327951 0.8160485

PDP-A estimates:

Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0102392 0.0154690 0.6619198 0.5084324
scale(IMS) -0.0273694 0.0146638 -1.8664580 0.0627639
ObserverPresent -0.0215384 0.0224029 -0.9614123 0.3369694
TaskWIT -0.0081381 0.0218764 -0.3720030 0.7101024
scale(IMS):ObserverPresent 0.0122012 0.0227213 0.5369929 0.5915935
scale(IMS):TaskWIT -0.0012590 0.0207378 -0.0607111 0.9516219
ObserverPresent:TaskWIT 0.0176881 0.0316825 0.5582936 0.5769798
scale(IMS):ObserverPresent:TaskWIT -0.0149861 0.0321328 -0.4663816 0.6412154

5. Make composite for anxiety in Study 2

Composite is composed of 8 items (standardized before averaged together), alpha = .91

Look at correlation between first and second blocks:

The correlation between the anxiety composite score on the first block and the second block is 0.9098042.

8. Look at relationship between anxiety and PDP-A/PDP-C

Anxiety composite scores were averaged across blocks, so each participant has one anxiety score per task.

## Saving 7 x 5 in image
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: MeanC ~ scale(Anx_composite) * Task + (1 | Subject)
##    Data: s2.wide
## 
## REML criterion at convergence: -136.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.09061 -0.49271  0.03496  0.55697  1.95890 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Subject  (Intercept) 0.03381  0.1839  
##  Residual             0.01764  0.1328  
## Number of obs: 386, groups:  Subject, 193
## 
## Fixed effects:
##                               Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)                    0.33925    0.01633 266.70000  20.769  < 2e-16 ***
## scale(Anx_composite)          -0.04235    0.01469 377.00000  -2.884  0.00415 ** 
## TaskWIT                        0.06763    0.01355 191.20000   4.991 1.35e-06 ***
## scale(Anx_composite):TaskWIT  -0.02641    0.01399 196.70000  -1.889  0.06043 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sc(A_) TskWIT
## scl(Anx_cm) -0.031              
## TaskWIT     -0.415  0.058       
## sc(A_):TWIT  0.014 -0.455  0.002

## Saving 7 x 5 in image
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: AResid ~ scale(Anx_composite) * Task + (1 | Subject)
##    Data: s2.wide
## 
## REML criterion at convergence: -331.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.36687 -0.65794 -0.04769  0.60500  2.60405 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Subject  (Intercept) 0.005595 0.0748  
##  Residual             0.018353 0.1355  
## Number of obs: 386, groups:  Subject, 193
## 
## Fixed effects:
##                                Estimate Std. Error         df t value Pr(>|t|)
## (Intercept)                  -4.377e-04  1.115e-02  3.622e+02  -0.039    0.969
## scale(Anx_composite)          1.421e-02  1.096e-02  3.786e+02   1.296    0.196
## TaskWIT                       3.064e-03  1.380e-02  1.912e+02   0.222    0.825
## scale(Anx_composite):TaskWIT  1.089e-02  1.403e-02  2.104e+02   0.776    0.438
## 
## Correlation of Fixed Effects:
##             (Intr) sc(A_) TskWIT
## scl(Anx_cm) -0.033              
## TaskWIT     -0.619  0.032       
## sc(A_):TWIT  0.021 -0.624  0.001

9. Look at relationship between IMS and anxiety, as a function of observer

## Warning: Removed 6 rows containing non-finite values (stat_smooth).
## Warning: Removed 6 rows containing missing values (geom_point).

## Warning: Removed 6 rows containing non-finite values (stat_smooth).

## Warning: Removed 6 rows containing missing values (geom_point).
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: scale(Anx_composite) ~ scale(IMS) * Observer * Task + (1 | Subject)
##    Data: s2.wide
## 
## REML criterion at convergence: 853.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.16647 -0.41242 -0.03104  0.41614  2.71661 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Subject  (Intercept) 0.8195   0.9053  
##  Residual             0.1543   0.3929  
## Number of obs: 380, groups:  Subject, 190
## 
## Fixed effects:
##                                     Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)                          0.05536    0.10002 217.78000   0.554 0.580487    
## scale(IMS)                           0.32910    0.09481 217.78000   3.471 0.000625 ***
## ObserverPresent                      0.01621    0.14485 217.78000   0.112 0.910999    
## TaskWIT                             -0.06212    0.05631 186.00000  -1.103 0.271398    
## scale(IMS):ObserverPresent          -0.29884    0.14691 217.78000  -2.034 0.043146 *  
## scale(IMS):TaskWIT                  -0.12604    0.05338 186.00000  -2.361 0.019257 *  
## ObserverPresent:TaskWIT             -0.03449    0.08155 186.00000  -0.423 0.672846    
## scale(IMS):ObserverPresent:TaskWIT   0.15425    0.08271 186.00000   1.865 0.063769 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sc(IMS) ObsrvP TskWIT sc(IMS):OP s(IMS):T OP:TWI
## scale(IMS)   0.129                                                 
## ObsrvrPrsnt -0.690 -0.089                                          
## TaskWIT     -0.282 -0.036   0.194                                  
## scl(IMS):OP -0.083 -0.645  -0.030  0.023                           
## s(IMS):TWIT -0.036 -0.282   0.025  0.129  0.182                    
## ObsrvP:TWIT  0.194  0.025  -0.282 -0.690  0.008     -0.089         
## s(IMS):OP:T  0.023  0.182   0.008 -0.083 -0.282     -0.645   -0.030

10. Look at relationship between EMS and anxiety, as a function of observer

## Warning: Removed 6 rows containing non-finite values (stat_smooth).
## Warning: Removed 6 rows containing missing values (geom_point).

## Warning: Removed 6 rows containing non-finite values (stat_smooth).

## Warning: Removed 6 rows containing missing values (geom_point).
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: scale(Anx_composite) ~ scale(EMS) * Observer * Task + (1 | Subject)
##    Data: s2.wide
## 
## REML criterion at convergence: 850.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.27546 -0.40978 -0.01832  0.44454  2.53021 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Subject  (Intercept) 0.7796   0.8830  
##  Residual             0.1591   0.3988  
## Number of obs: 380, groups:  Subject, 190
## 
## Fixed effects:
##                                      Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)                          0.008509   0.097376 220.150000   0.087 0.930449    
## scale(EMS)                           0.343958   0.102343 220.150000   3.361 0.000916 ***
## ObserverPresent                      0.068828   0.140705 220.150000   0.489 0.625210    
## TaskWIT                             -0.045014   0.056690 186.000000  -0.794 0.428180    
## scale(EMS):ObserverPresent          -0.142602   0.140972 220.150000  -1.012 0.312859    
## scale(EMS):TaskWIT                   0.011562   0.059581 186.000000   0.194 0.846342    
## ObserverPresent:TaskWIT             -0.047481   0.081914 186.000000  -0.580 0.562855    
## scale(EMS):ObserverPresent:TaskWIT  -0.022435   0.082070 186.000000  -0.273 0.784873    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) sc(EMS) ObsrvP TskWIT sc(EMS):OP s(EMS):T OP:TWI
## scale(EMS)  -0.006                                                 
## ObsrvrPrsnt -0.692  0.004                                          
## TaskWIT     -0.291  0.002   0.201                                  
## scl(EMS):OP  0.004 -0.726   0.000 -0.001                           
## s(EMS):TWIT  0.002 -0.291  -0.001 -0.006  0.211                    
## ObsrvP:TWIT  0.201 -0.001  -0.291 -0.692  0.000      0.004         
## s(EMS):OP:T -0.001  0.211   0.000  0.004 -0.291     -0.726    0.000

11. Look at relationship between IMS-EMS and anxiety, as a function of observer

## Warning: Removed 6 rows containing non-finite values (stat_smooth).
## Warning: Removed 6 rows containing missing values (geom_point).

## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: scale(Anx_composite) ~ scale(IMS.EMS.diff) * Observer * Task +      (1 | Subject)
##    Data: s2.wide
## 
## REML criterion at convergence: 862.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1945 -0.4221 -0.0138  0.4133  2.5022 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Subject  (Intercept) 0.8482   0.921   
##  Residual             0.1568   0.396   
## Number of obs: 380, groups:  Subject, 190
## 
## Fixed effects:
##                                               Estimate Std. Error         df t value Pr(>|t|)
## (Intercept)                                   0.008219   0.101134 217.250000   0.081    0.935
## scale(IMS.EMS.diff)                          -0.027382   0.103972 217.250000  -0.263    0.793
## ObserverPresent                               0.081193   0.146152 217.250000   0.556    0.579
## TaskWIT                                      -0.052872   0.056492 186.000000  -0.936    0.351
## scale(IMS.EMS.diff):ObserverPresent          -0.118671   0.146224 217.250000  -0.812    0.418
## scale(IMS.EMS.diff):TaskWIT                  -0.094283   0.058077 186.000000  -1.623    0.106
## ObserverPresent:TaskWIT                      -0.041573   0.081638 186.000000  -0.509    0.611
## scale(IMS.EMS.diff):ObserverPresent:TaskWIT   0.116359   0.081678 186.000000   1.425    0.156
## 
## Correlation of Fixed Effects:
##                 (Intr) sc(IMS.EMS.) ObsrvP TskWIT sc(IMS.EMS.):OP s(IMS.EMS.):T OP:TWI
## sc(IMS.EMS.)     0.086                                                                
## ObsrvrPrsnt     -0.692 -0.060                                                         
## TaskWIT         -0.279 -0.024        0.193                                            
## sc(IMS.EMS.):OP -0.061 -0.711       -0.003  0.017                                     
## s(IMS.EMS.):T   -0.024 -0.279        0.017  0.086  0.199                              
## ObsrvP:TWIT      0.193  0.017       -0.279 -0.692  0.001          -0.060              
## s(IMS.EMS.):OP:  0.017  0.199        0.001 -0.061 -0.279          -0.711        -0.003